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Realizability Games in Arithmetical Formulae.

Abstract : This work is devoted to Krivine's Realizability, focusing over computational aspects of realizers. Each formula has associated a game. Each proof of a formula gives a term implementing a winning strategy for the game associated to the proven formula. A proof is, by soundness, a combinator capable to take winning strategies of the premises and furnish a winning strategy for the conclusion. Are treated the following topics: A. The specification problem, which consists in characterize all realizers of a given formula in computational terms. Many examples are given. B. We study a proof as a combinator of winning strategies: Consider an implication $A\to B$ where $A$ and $B$ are $\Sigma^0_2$ formulae. Consider $C$ the prenex normal form of the implication $A\to B$. We study a proof of $A, C\to B$ as a combinator of winning strategies. In order to do this work, some techniques where developed to trace the execution of processes, in particular the so called "threads method".
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https://tel.archives-ouvertes.fr/tel-00594974
Contributor : Mauricio Guillermo <>
Submitted on : Monday, May 23, 2011 - 3:00:51 AM
Last modification on : Saturday, March 28, 2020 - 2:17:47 AM
Long-term archiving on: : Wednesday, August 24, 2011 - 2:22:42 AM

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  • HAL Id : tel-00594974, version 1

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Mauricio Guillermo,. Realizability Games in Arithmetical Formulae.. Mathematics [math]. Université Paris-Diderot - Paris VII, 2008. English. ⟨tel-00594974⟩

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